Can the world, or thinking, that is called spirit in mind, body and
spirit, be broken down into clear and identifiable parts, hierarchy or
components? Can such simplicity be reached? If so, what are they
please?

Anything spiritual or supernatural cannot be verified scientifically,
so there's no way to show that a spirit exists, let alone what
structure it may have. Even the mind can only be explained by the
different parts of the brain that account for it.

See also http://www.skepdic.com/soul.html

According to the Bible, the "Spirit" is a gift from God. Genesis
2;7.."And Jehovah God [ personal name and title] proceeded to form the
man out of the dust from the ground AND TO BLOW INTO HIS NOSTRILS THE
BREATH OF LIFE, and the man came to BE a living soul". It is
interesting that Genesis 1;24 indicates that animals were created and
present on the earth, BEFORE Adam was created. Verse 24 says " And God
went on to say, " Let the earth put forth living souls  according to
their kinds, domestic animal and moving animal and wild beastsof the
earth according to its kind"...and it came to be so. There are two
very interestin scriptures, when applied, gives good insight into the
subject of the "soul". God did not give man a separate soul, but man
"came to be" a living soul.
Ezekiel 18;4.."Look! All the souls- to me they belong. As the soul of
the father so likewise the soul of the son-to me they belong. The soul
that is sinning-it itself will die".
Ecclesiastes 3;19.."There is an eventuality as respects the sons of
mankind and an eventuality as respects the beast, and they have THE
SAME eventuality. As the one dies, so the other dies, and they all
have BUT ONE spirit [ Hebrew=ru'ach].
Psalm 146;4.." His spirit [Hebrew/ru'ach] goes out, he goes back to
his ground; in that day his thoughts do perish".